{"id":1317,"date":"2011-11-16T09:33:13","date_gmt":"2011-11-16T00:33:13","guid":{"rendered":"http:\/\/www.qcri.or.jp\/lab\/?page_id=1317"},"modified":"2024-12-19T14:50:18","modified_gmt":"2024-12-19T05:50:18","slug":"directly-solving-2nd-order-density-matrix","status":"publish","type":"page","link":"https:\/\/qcri.or.jp\/lab_en\/english\/research\/directly-solving-2nd-order-density-matrix","title":{"rendered":"Direct Determination of 2-RDM"},"content":{"rendered":"

Directly solving 2nd-order reduced density matrices without using wavefunctions<\/h3>\n
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\u00a0 \u00a0Since any basic operators of properties include only one- and two-electron operators, all the properties of molecules can be calculated if the exact second-order density matrices are given. The second-order density matrix depends only on 4 electron coordinates at maximum. Therefore, we may construct quantum mechanics using the second-order density matrix as a basic variable instead of the wave function (Wave Mechanics without Wave).<\/div>\n

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\u00a0 \u00a0Nakatsuji presented in 1976 a basic equation called density equation (or later called contracted Schr\u00f6dinger equation, again in the West World) which is equivalent to the Schr\u00f6dinger equation in the space of the density-matrix. In 1996, by improving Valdemoro’s theory, Nakatsuji and Yasuda firstly solved the density equation for real molecules. In 2001, Nakatsuji and Nakata further invented a variational method for directly solving the second-order density matrices of molecules using positive semi-definite programming (SDP) algorithm. This method was further shown to be stable under the multi-reference and strong-correlation situations.<\/div>\n
\n\"DMT\"<\/div>\n
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References<\/strong><\/div>\n